91 lines
2.2 KiB
Python
91 lines
2.2 KiB
Python
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def product(numbers):
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r = 1
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for n in numbers:
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r = r * n
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return r
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def _incrementer():
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""" Generator function that returns natural numbers where the higher
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digits are smaller or equal than the lower digits. """
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n_digits = 2
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r = [1] * n_digits
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while True:
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yield r
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incremented = False
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for i in range(n_digits - 1):
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if r[i] < r[i + 1]:
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r[i] += 1
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incremented = True
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for j in range(i):
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r[j] = 1
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break
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if incremented:
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continue
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elif r[-1] < 2000:
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r[-1] += 1
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for j in range(n_digits - 1):
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r[j] = 1
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else:
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n_digits += 1
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r = [1] * n_digits
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for k in range(40, 50):
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s = product_sum_number(k)
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print("k={}: {} = {}".format(k, product(s), s))
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def product_sum(k):
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# Create initial list of canditates
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canditates = []
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for n in range(2, k + 1):
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rest_sum = k - n
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if rest_sum + n * 2 < 2 ** n:
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break
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canditates.append(tuple([2 for _ in range(n)]))
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processed = set(canditates)
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solutions = []
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while canditates:
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numbers = canditates.pop()
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processed.add(numbers)
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s = k - len(numbers) + sum(numbers)
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p = product(numbers)
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if s == p:
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solutions.append(numbers)
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elif s > p:
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for i in range(len(numbers) - 1):
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if numbers[i] < numbers[i + 1]:
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n = list(numbers)
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n[i] += 1
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t = tuple(n)
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if not t in processed:
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canditates.append(t)
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n = list(numbers)
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n[-1] += 1
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t = tuple(n)
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if not t in processed:
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canditates.append(t)
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else:
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pass
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result = min([product(ns) for ns in solutions])
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return result
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def euler_088():
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ns = set()
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for k in range(2, 12001):
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r = product_sum_2d(k)
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print("k={}: {}".format(k, r))
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ns.add(r)
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return sum(ns)
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if __name__ == "__main__":
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solution = euler_088()
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print("e088.py: " + str(solution))
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assert(solution == 7587457)
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